Polysemous nouns have closely related senses that denote different types of entities. For instance lunch can denote an eventuality (eating lunch) or a physical entity (the food eaten). Furthermore, polysemous nouns can be felicitous in copredication constructions such as (1) that arguably elicit both of these senses simultaneously.

(1) Lunch was delicious and lasted for two hours.

Data such as (1) have been claimed to pose a problem for canonical approaches to formal semantics in the Frege-Church-Montague tradition (see e.g., Chomsky 2000). For instance, given an assumption that lunch eating events and food are members of the domains of different semantic types, it can be shown that there is no set characterisable in simply typed lambda calculus that has as members entities that are lunch-eating eventualities and/or food.

This talk looks at two responses to the challenge of polysemy. A large number of analyses of polysemy go for an enrichment of the type theory, and so add structure. A lesser known option, I suggest, is to impoverish the type theory. This can be implemented within a mono-typed semantics as developed in e.g., Liefke 2014, Liefke & Werning 2018. However, I suggest there are reasons for why the latter approach still needs to make use of the kind of extra structure utilised by the former, even if this is not introduced in the type theory. I then discuss how distinct these two approaches may turn out to be.